EFFECT OF Mn3+ ION ORBIT LATTICE COUPLING ON MAGNETIC ANISOTROPY OF MnxFe3-xO4 SYSTEM

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EFFECT OF Mn3+ ION ORBIT LATTICE COUPLING ON MAGNETIC ANISOTROPY OF

MnxFe3-xO4 SYSTEM

P. Novák, V. Roskovec, Z. Šimša, V. Brabers

To cite this version:

P. Novák, V. Roskovec, Z. Šimša, V. Brabers. EFFECT OF Mn3+ ION ORBIT LATTICE COU- PLING ON MAGNETIC ANISOTROPY OF MnxFe3-xO4 SYSTEM. Journal de Physique Colloques, 1971, 32 (C1), pp.C1-59-C1-61. �10.1051/jphyscol:1971114�. �jpa-00213958�

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JOURNAL DE PHYSIQUE Colloque C I, supplkment au no 2-3, Tome 32, Fkvrier-Mars 1971, page C 1 - 59

EFFECT OF Mn3+ ION ORBIT LATTICE COUPLING ON MAGNETIC ANISOTROPY OF Mn,Fe3 - ,04 SYSTEM

P. NOVAK, V. ROSKOVEC, Z. SIMSA

Institute of Solid State Physics, Czechoslovak Acad. Sci., Prague, Czechoslovakia and V. A. M. BRABERS

Technical University, Eindhoven, The Netherlands

R&umk. - L'anisotropie magnetique des cristaux MnzFe3-zO* (x = 0,99,1,24, 1,6) a kt6 mesurke ~usqu'tl 4,2 OK par mesure de couple. L'analyse de Fourier de ces courbes de couple dans les plans (loo), (110) et (11 1) lnd~que que, dans ces ferrites, il est impossible de dkcrire la partie anisotrope de l'knergie libre seulement par les deux premikres constantes d'anisotropie cubique. L'explication de ce comportement anormal est donnke par les interactions fortes entre les electrons de l'ion Mn3f et le rkseau cristallin (effet Jahn-Teller fort).

Abstract. - Magnetic anisotropy of the MnzFep-z04 (x = 0.99, 1.24, 1.6) single crystals was measured down to liquid helium temperatures using the torque method. Fourier analysis of the torque curves in the (loo), (1 10) and (1 11) crystallographic planes showed that in these ferrites the anisotropic part of the free energy cannot be properly described by means of the first and the second cubic anisotropy constants only.

The explanation of this anomalous behaviour is given taking into account that there is a strong coupling between the electrons of the Mn3+ ion and the crystal lattice (strong Jahn-Teller-effect).

1. Introduction. - Recently, the experimental found temperature dependences of the first anisotropy cons- tant in the MnxFe3-,04 system [l] for x > 1 were explained by the Jahn-Teller effect of the octahedral Mn3+-ions [2]. To check this hypothesis we have studied the temperature dependences of the higher anisotropy constants, which were not treated in these materials up to now neither experimentally, nor theoretically.

The free energy of a cubic ferromagnetic crystal is expressed in a form

F = F , + K , ( ~ ~ ag+af ai+ag a:)+K2 a: a; a:+... (1) where ai represent the direction cosines of the magnetization referred to the cubic axes. Experimental torque can be develo~ed in a Fourier series

L = - - - = a aF

a ~ ,

^o

+ C

[a, sin (nq)

+

b, cos (nq)] . (2)

n

In a special case of (110) plane, if q is the angle between the direction of magnetization and [OOl] direction and the series (1) is well approximated by the first three terms only, the coefficients b, = 0 and the anisotropy constants can be determined by

If K , = K; the abovementioned approximation appears to be sufficient, otherwise the higher terms in (1) should be taken into account.

2. Experimental procedure and results. - Magne- tic anisotropy was measured on polished spheres of about 3 mm in diameter mounted in an automatic compensated torque anisometer described elsewhere [3]. Most of the measurements have been made in magnetic field of 15 kOe in (1 10) plane, for comparison the measurements in (100) and (1 11) planes were also

performed. To analyse the torque curves, the values of L, were gathered for 65 angles q, = kn/32 (k = 0, 1 ... 64). After the correction for noncolinearity of the magnetization and the external field H was made, the coefficients a,, b, in (2) were found by means of a computer. Afterwards the anisotropy constants K,, K2, K; were calculated.

FIG. 1. - Temperature dependence of the anisotropy constants for

Mno,99Fez,0104

In figure 1 the temperature dependences of K' s are plotted for the sample x = 0.99. The course of K, is in a qualitative accord with Palmer's measurements [I], the differences being attributed to a slight iron excess in our sample. The most striking result is the large difference between K2 and Ki. This difference is even larger for the composition x = 1.24 the results of which are represented in figure 2. Very good agree-

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1971114

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P. NOVAK, V. ROSKOVEC, Z. SIMSA AND V. A. M. BRABERS

FIG. 2 . - Temperature dependence of the anisotropy constants for

Mn1.24Fe1.7604.

ment of Palmer's data with our determination of K, in (001) plane is seen, while the absolute values of K, as determined from (110) plane are somewhat less.

This fact together with the differences between K, and K; indicate that higher terms in the series (1) are not insignificant. The same holds for the sample x ⁼1.6 the anisotropy constants of which are shown in figure 3.

FIG. 3. - Temperature dependence of the anisotropy constants for

Mnl.sFe1.404.

3. Discussion. - Octahedrally coordinated Mn3"

ion tends to remove the orbital degeneracy of the ground state by distorting its environment. We assume that the degeneracy is removed by a tetragonal distortion along one of the cubic axes. As the three cubic axes are equivalent and spin of Mn3+ ion equals 2, there are fifteen low lying states I a, M

>

of the system considered (a = x , y, z ; M = - 2, - 1

...

^2).

The Hamiltonian appropriate to describe the split-

ting of this multiplet in the presence of magnetization and random strains is

;re = gPH,,. S 4-

s:-2 0

0 s,2-2

0 0

s:

- 2 0 0 6 , The first term in (4) represents the exchange interactions, the second the coupling between Mn3+ ion spin and axial distortion and the third the splitting by random strains.

From the Curie temperature of Mn,O, the value PHex is estimated to be of the order of ten cm-l.

Theoretical prediction as well as EPR data [4] give 2 cm-I < 1 D 1 < 4 cm-I. The splitting by random strains varies from site to site ; for simplicity let us consider two limiting cases only :

a) UNSTABILIZED JAHN-TELLER EFFECT. - If there is no random strain, then the energy levels of the three lowest lying states x, - 2

>,

( y , - 2

>,

^(z,- 2

>

mutually intersect when the magnetization is rotated.

Anisotropy constants, which correspond to such;"a case are linearly proportional to D and consequently very large at low temperatures. They are very strongly temperature dependent due to the small energy interval between the states I ^x,- 2

>,

^{( y ,}^-²

>,

⁽^z,- 2

>.

b) STRAIN STABILIZED JAHN-TELLER ^EFFECT:- Let in (4) 6, % gPH,, ; 6, = 6, = 0. The states ( z, M

>

are then separated from the states 1 x, M

>

^and

I y, M

>

by a large energy interval. At temperature not too high only the states having z as a distortion axis are populated. Such a situation clearly corres- ponds to what was previously called a static Jahn- Teller effect. Corresponding anisotropy constants may then be determined by a perturbation procedure [ 5 ] .

The temperature dependences of KJN, K,/N, K ~ / N

FIG. 4. - Theoretically calculated temperature dependence of the one-ion anisotropy constants of Mn3+ ion. Parameter

D = 2.5 cm-1, pH = 25 cm-1.

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EFFECT OF Mn3+ ION ORBIT LATTICE COUPLING C 1 - 6 1 for unstabilized and strain-stabilized ~ a h n - ~ e l l e r

effect are displayed in figure 4. Qualitative analysis of the experimental data shows that for most of the Mn3+ ions the Jahn-Teller effect is strain stabilized.

There are some of the Mn3+ ions, however, for which the random strains are small. If figure 4 is confron- ted, it is seen that these ions are responsible for the minimum of K, and for the sudden decrease of K, at low temperature. Stoichiometric manganese ferrite has partially inverse structure, which invokes large strains. In Mn, .,Fez .,O, the increase in concentration

of Mn3+ ions is also accompanied by large local strains. We expect therefore the unstabilized Jahn- Teller effect to be the most effective for the sample with x = 1.24. This is also supported by (the experi- ment.

Preliminary calculations have shown that the difference between K, and K;, wich appears for all three samples may be explained if the perturbation procedure for strain stabilized Mn3 ⁺ion is carried to higher orders and if the spin canting is also taken into account.

More details will be published elsewhere.

References

[I] PALMER (W.), J. Appl. Phys., 1962, 33, 1201s [4] GERRITSEN (H. J.), SABISKY (E. B.), Phys. Rev., 1963, [Z] NOVAK (P.), Czech. J. Phys., 1970, B 20, 220. 132,1507.

133 GERBER (R.), VIL~M (F.), J. Sci. Instr. (J. Phys. E.), [S] Sec e.g. STURGE (N. D.) et a]., Phys. Rev., 1969, 180,

1968, 1, 389. 413.